Quantitative Ap...

A can of paint thinner containing chemicals X and Y in the ratio 7:2 is placed beside a beaker filled with 80% acid solution. It is known that 20% of chemical X and 10% of chemical Y evaporate every hour, while 30% of the acid and 10% of water in the beaker evaporate every hour. After six hours, the contents of the can of paint thinner and the beaker are inspected only to find that the ratio of chemical X to chemical Y is ‘$$k^5$$’ times the ratio of acid to water in the beaker. Which of the following correctly represents $$k$$?

In triangle PQR, PQ=12cm, QL and RN are altitudes on PR and PQ respectively. If PL=8cm and area of quadrilateral QRLN =40 cm². Find the area of triangle PQR (in cm$$^2$$)

In triangle ABC, BC = $$ 7 + 7\sqrt{3} $$. Also Angle ABC = 45°, Angle ACB = 30°. What is the area of the triangle ABC?

In the given figure it is known that O is the center of the circle. PQ and RS are two chords which intersect at right angles such that PM=6cm, MQ=4cm and MS=12cm. Find the area of shaded region.(Take $$^{ }\pi\ $$=3.14).

Two cards are drawn from a pack of cards. What is the probability that none of these cards is either black or a face card?

A manager allots P,Q,R some work to finish. Their efficiencies are in the ratio 1:2:3 while their hourly wages are in the ratio 4:6:11. After completion of 25% of the job, the manager had to fire one of the workers due to some constraints. Whom should he fire to ensure that the work is done in the cheapest possible way ?

The Jan Shadabti Express reached 36 minutes late from its scheduled time in Ludhiana. If the train manages to reach its final station - Jalandhar at the scheduled time itself by increasing its speed by 66.67% over its original speed, then find the normal time (in hrs) taken by the train to travel from Ludhiana to Jalandhar?

Three test tubes - marked A, B and C - contain silver and nitric acid in the ratio p:q such that p∊{1,3,4,7} and q∊{8,11,13,15}. If a scientist is told that A, B and C can take any value of p and q, and are mixed together, for how many distinct sets of values of concentration of the test tubes A, B and C will the resultant solution have a silver to nitric acid ratio of 1:1?

Harry has t-shirts of Pepe, Levis and Adidas in the ratio of 5:1:4. On Ron's birthday, Harry gifted Ron some t-shirts of Pepe and Adidas. As a result, the ratio of t-shirts of Pepe, Levis and Adidas with Harry now becomes 5:3:7. What is the minimum total number of t-shirts that Harry had initially?

In how many ways can ten persons be seated on chairs numbered 1 to 10 such that 2 particular persons A and B always sit adjacent to each other and 1 particular person C does not sit adjacent to A and B.

A milkman uses an inverted conical container, with a radius to depth ratio of 5:12, to measure and sell milk. While he sells the milk at its cost price, his customers are unaware that the conical bucket contains a circular airtight base plate effectively reducing the depth by 33.33% as shown in the figure. What is his profit percentage?

Due to a fire, x% of Ramesh’s grain got destroyed. To cover up the expenses, he marked up the price of his remaining grain by 50%. After selling half of the unburnt grain at 50% markup, he lowers the markup and sells the remaining grain at 30% markup.

While reconciling at the end of the day, Ramesh realised that the profit generated by selling the grain at 50% markup was equal to the loss suffered from the grain that got destroyed. What is Ramesh’s overall approximate profit percentage(to the nearest integer)?

Pranay borrowed Rs 54,735 from Vinay at the interest rate of 30% for three years. He repaid the money in three instalments paying each instalment at the end of each year. The three instalments are in A.P, with the second instalment being 40% less than the first. What is the average value of the 3 instalments? (Round it to the nearest integer)

For how many integral values of ‘x’ does the inequality (x+1)(x+3)(x+5)…(x+99) < 0 hold good?

Ram and Lakhan started running towards each other from opposite ends of a straight road. Ram started at 11 am while Lakhan started at 2 pm and met Ram for the first time at point ‘O’ on the road. They continued running till they reached opposite ends. Immediately after that, they changed the direction towards their starting point and again met at the same point ‘O’. If they met for the first time at 3 pm, then what is the ratio of the speed of Lakhan to that of Ram?

The sum of squares of two positive integers is twenty-five times the larger number and the difference of squares of the positive integers is seven times the larger number. Find the smaller number.

Find the sum of all possible values of x where: $$\log_{10}x+\log_{10}(x-7)+\log_{10}5-\log_{10}3=2$$

An equilateral triangle whose perimeter = 36 cm, is rotated about its side to form a closed solid figure. Find the volume of the solid so formed.

The sum of the series: $$\frac{7}{15} + \frac{77}{15^2} + \frac{777}{15^3} + \frac{7777}{15^4} + $$…. is

Ram can do a piece of work in 15 days. Shyam can do the same piece of work in 20 days. They work together for 5 days and then Ram leaves. On which day (from the beginning) will the work be completed?

X and Y are prime numbers (X>Y) such that X-Y and X+Y are also prime. How many natural number divisors does Z = X*Y+2 have?

All the people of a village attended a rally organized by a political leader. They used bullock-carts for transportation. Half way to the rally, 20 bullock-carts broke down, so each of the other bullock-carts had to carry 2 extra people. On the return journey, 30 more bullock-carts broke down, so each of the remaining bullock-carts had to carry 6 more people than when they started out in the morning. Determine the number of people who attended the rally.